SOLUTION: in right triangle DEF, angle D eguals 90 and angle F is 12 degrees less than twice angle E. find angle E

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Question 381169: in right triangle DEF, angle D eguals 90 and angle F is 12 degrees less than twice angle E. find angle E
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of the three measures of a triangle is ALWAYS 180.

So, we know that D+E+F=180

D=90, so we know that 90+E+F=180 thus

E+F=90

Also, we are given

F+12=2*E

F+12=2E

F=2E-12

Therefore, substituting for F back into E+F=90 gives us

E+(2E-12)=90

3E-12=90

3E=102

E=34

So angle E is 34 degrees, which is the answer.

In additon, since we know that E+F=90 then we have

34+F=90

F=56

I hope this helps!